The launch took place on Monday within hours of Australia and Fiji signing a new mutual defence alliance, known as the Ocean of Peace treaty, in Suva.
Chinese state media said the test was a missile topped with a dummy warhead as part of annual military training.
Foreign Minister Penny Wong said Australia had made it clear to Beijing it considered the test fire "destabilising" to the region.
She confirmed Australia had been warned by China beforehand.
Mr Albanese will visit Honiara on Tuesday, where he will meet with his Solomon Islands counterpart Matthew Wale to progress talks on a new treaty.
Mr Wale has previously called for a Pacific-wide pact.
The Ocean of Peace Alliance which views an attack on one nation as an attack on the other, marks Fiji's first-ever alliance.
Fiji has become Australia's fourth ally, alongside the US, New Zealand and Papua New Guinea.
The treaty allows other Pacific nations to join the alliance.
The agreement was signed alongside the Vuvale Union, which will invest $1 billion over the next decade into key areas including climate and economic initiatives.
During a joint press conference with Mr Albanese, Fijian Prime Minister Sitiveni Rabuka said he did not anticipate any "severe pushback" from China.
"I believe that they will welcome the understanding that it is within Australia and Fiji," he told reporters.
"It does not threaten Fiji's relationship with China nor Australia's relationship with China. And as we have made it very clearly in the past, your enemies are not necessarily my enemies."
Later on Monday, Mr Albanese and Mr Rabuka attended an evening event at the Australian High Commission in the Fijian capital.
The prime minister announced that Australia will increase its investment in the Fijian Drua rugby union team, but did not specify an amount.
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